Coincidence?

1 lowly point per pawn gives this:

Mathematics

Mathematically, 1 is:

• in arithmetic (algebra) and calculus, the natural number that follows 0 and precedes 2 and the multiplicative identity of the integers, real numbers and complex numbers;
• more generally, in abstract algebra, the multiplicative identity ("unity"), usually of a ring.

One cannot be used as the base of a positional numeral system; sometimes tallying is referred to as "base 1", since only one mark (the tally) is needed, but this is not a positional notation.

The logarithms base 1 are undefined, since the function 1^x always equals 1 and so has no unique inverse.

In the real-number system, 1 can be represented in two ways as a recurring decimal: as 1.000... and as 0.999... (q.v.).

Formalizations of the natural numbers have their own representations of 1:

• in the Peano axioms, 1 is the successor of 0;
• in Principia Mathematica, 1 is defined as the set of all singletons (sets with one element);
• in the Von Neumann cardinal assignment of natural numbers, 1 is defined as the set {0}.

In a multiplicative group or monoid, the identity element is sometimes denoted 1, especially in abelian groups, but e (from the GermanEinheit, "unity") is more traditional. However, 1 is especially common for the multiplicative identity of a ring, i.e., when an addition and 0 are also present. When such a ring has characteristic n not equal to 0, the element called 1 has the property that n1 = 1n = 0 (where this 0 is the additive identity of the ring). Important examples are general fields.

One is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few.

In many mathematical and engineering equations, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters.

Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must equal 1.

It is also the first and second numbers in the Fibonacci sequence (0 is the zeroth) and is the first number in many other mathematical sequences. As a matter of convention, Sloane's early Handbook of Integer Sequences added an initial 1 to any sequence that did not already have it and considered these initial 1's in its lexicographic ordering. Sloane's laterEncyclopedia of Integer Sequences and its Web counterpart, the On-Line Encyclopedia of Integer Sequences, ignore initial ones in their lexicographic ordering of sequences, because such initial ones often correspond to trivial cases.

One is neither a prime number nor a composite number, but a unit, like -1 and, in the Gaussian integers, i and -i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units (e.g., 4 = 2² = (-1)⁶×1²³×2²).

The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of characteristic 1. Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all.

One is the only positive integer divisible by exactly one positive integer (whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers). One was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by one and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units.

One is one of three possible values of the Möbius function: it takes the value one for square-free integers with an even number of distinct prime factors.

One is the only odd number in the range of Euler's totient function φ(x), in the cases x = 1 and x = 2.

One is the only 1-perfect number (see multiply perfect number).

By definition, 1 is the magnitude or absolute value of a unit vector and a unit matrix (more usually called an identity matrix). Note that the term unit matrix is sometimes used to mean something quite different.

By definition, 1 is the probability of an event that is almost certain to occur.

One is the most common leading digit in many sets of data, a consequence of Benford's law.

The ancient Egyptians represented all fractions (with the exception of 2/3 and 3/4) in terms of sums of fractions with numerator 1 and distinct denominators. For example, . Such representations are popularly known as Egyptian Fractions or Unit Fractions.

The Generating Function that has all coefficients 1 is given by

.

This power series converges and has finite value if and only if, .

[edit]Table of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000
	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000

Division	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15
	1	0.5	0.3	0.25	0.2	0.16	0.142857	0.125	0.1	0.1		0.09	0.083	0.076923	0.0714285	0.06
	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20
	1	1	1	1	1	1	1	1	1	1		1	1	1	1	1	1	1	1	1	1
	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20

[edit]In technology

• The resin identification code used in recycling to identify polyethylene terephthalate^[2]
• Used in binary code along with 0

[edit]In science

• The atomic number of hydrogen

[edit]In philosophy

In the philosophy of Plotinus and a number of other neoplatonists, The One is the ultimate reality and source of all existence. Philo of Alexandria (20 B.C.-50 C.E.) Philo regards number one as God's number, and the basis for all numbers ("De Allegoriis Legum," ii.12 [i.66]).

[edit]In fiction

• The characters Thomas the Tank Engine, Skarloey and Godred from the book series The Railway Series and Thomas and Friends have this number.
• Numbuh 1, a character from the TV series Codename: Kids Next Door.
• The character Francesco Bernoulli from the animated feature film Cars 2 is numbered 1.
• Mr. One from the Japanese comics series One Piece.
• The General Lee from the TV series The Dukes of Hazzard is numbered 01.
• Christopher Pike, the Captain of the Enterprise on the original Star Trek pilot "The Cage", calls his first officer (played by Majel Barrett) "Number One". On the sequel series Star Trek: The Next Generation, Jean-Luc Picard, Captain of the Enterprise-D, refers to his second-in-command, Will Riker, as Number One.

[edit]In sports

• 1 is the lowest number permitted for use by players of the National Hockey League (NHL), as the league has banned 00 and 0. (The highest number permitted is 98.)
• Many sports use 1 as their standard scoring increment—examples include goals in a large number of sports, runs in baseball and cricket, and points in volleyball. Examples where 1 is a non-standard increment, or used for one of several possible classes of scores, are listed below by sport.
• In Australian rules football, 1 point is awarded to the attacking team for a behind, scored when:
  • The ball is kicked by the attacking team and passes between a goal post (taller post) and the nearest behind post (shorter post) on the defensive side of the field without touching the behind post.
  • The ball passes between the defending team's goal posts, but either (1) was not kicked by the attacking team or (2) hit a goal post.
  • The defending team deliberately forces the ball between any two of its own posts. This particular score is officially called a "rushed behind".
• In baseball scoring, the number 1 is assigned to the pitcher.
• In basketball:
  • 1 point is awarded for a successful free throw.
  • In the 3×3 variant of the game, shots made from inside the "three-point" arc are also worth 1 point. (Shots from outside the arc are worth 2 points.)
  • The number 1 is used to designate the point guard position.
• In association football (soccer):
  • 1 point is awarded for a successful goal
  • The number 1 is often given to the goalkeeper
• In Gaelic football, hurling and camogie, a "point", with a scoring value of 1, is awarded when the attacking team legally sends the ball over the opponent's crossbar (above the goal).
• In gridiron football codes, one point is awarded under the following circumstances:
  • In almost all leagues, for a successful place kick after a touchdown. In American football, the score is formally known as a "try", although the terms "extra point", "conversion", "PAT" (for "point after touchdown"), and "point after" are far more commonly used. In Canadian football, the score is formally and popularly called a "convert". Conversions can also be scored by the now-rare drop kick; in standard American and Canadian football, such a conversion is worth 1 point, while most forms of indoor football, including theArena Football League, award 2 points for a drop-kicked conversion.
  • In college football, if a point after "try" is blocked, if the blocked ball stayed in the field of play a defender may pick up and run the ball to his end zone at the other end of the field for a one point safety.
  • In six-man football, one point is awarded for a successful conversion from scrimmage after a touchdown. Note that in standard 11-man (American) or 12-man (Canadian) football, place kicks are worth 1 point and conversions from scrimmage worth 2; this is reversed in six-man because the reduced number of players makes kicked conversions much more difficult.
  • In Canadian football only, a single or "rouge" is awarded when the ball is legally kicked into the opponent's end zone (except for a successful field goal), and the receiving team does not return, or kick, the ball out of its end zone. (In American football, the same play would result in a touchback and no points.)
  • Some forms of indoor football in the U.S. award a "single", similar to the Canadian score, on kickoffs only.
• In rugby league:
  • A drop goal is worth 1 point.
  • In most competitions (though not the European Super League, which uses static squad numbering), the starting fullback wears jersey number 1.
• In rugby union:
  • The starting loosehead prop wears the jersey number 1.
  • In the early years of the sport (prior to 1890), conversions, penalties, drop goals, and goals from mark were all worth 1 point. At that time, a try was worth no points, only giving the attacking team the right to attempt a conversion. In 1890–91, tries were rewarded with 1 point, while all other scores were increased in value. After that time, all scores have been worth at least 2 points (the goal from mark was abolished in 1977).
• The jersey number 1 has been retired by several North American sports teams in honor of past playing greats or other key figures (or, in one case, a team's fans):
  • In Major League Baseball:
    • The Boston Red Sox, for Hall of Famer Bobby Doerr.
    • The Cincinnati Reds, for manager Fred Hutchinson.
    • The Los Angeles Dodgers, for Hall of Famer Pee Wee Reese.
    • The New York Yankees, for Billy Martin, who both played for and managed the team.
    • The Philadelphia Phillies, for Hall of Famer Richie Ashburn.
    • The Pittsburgh Pirates, for manager Billy Meyer.
    • The St. Louis Cardinals, for Hall of Famer Ozzie Smith.
  • In the NBA:
    • The Boston Celtics, for founding owner Walter Brown, a member of the Hall of Fame as a contributor.
    • The Milwaukee Bucks

3 points is a minor piece:

In mathematics

• Three is the first odd prime number,^[1] and the second smallest prime. It is both the first Fermat prime (2²ⁿ + 1) and the first Mersenne prime (2ⁿ − 1), the only number that is both, as well as the first lucky prime. However, it is the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime (2! + 1), the second Lucas prime, the second Stern prime.
• Three is the first unique prime due to the properties of its reciprocal.
• Three is the aliquot sum of 4.
• Three is the third Heegner number.
• Three is the second triangular number and it is the only prime triangular number. Three is the only prime which is one less than a perfect square. Any other number which is n² − 1 for some integer n is not prime, since it is (n − 1)(n + 1). This is true for 3 as well, but in its case one of the factors is 1.
• Three non-collinear points determine a plane and a circle.
• Three is the fourth Fibonacci number. In the Perrin sequence, however, 3 is both the zeroth and third Perrin numbers.
• Three is the fourth open meandric number.
• Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions, (.000..., .333..., .666...)
• A natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc..). See also Divisibility rule. This works in base 10 and in any positional numeral system whose base divided by three leaves a remainder of one (bases 4, 7, 10, etc.).
• A triangle is the only figure which, if all endpoints have hinges, will never change its shape unless the sides themselves are bent.
• 3 is the smallest prime of a Mersenne prime power tower 3, 7, 127, 170141183460469231731687303715884105727. It is not known whether any more of the terms are prime.
• Three of the five regular polyhedra have triangular faces — the tetrahedron, the octahedron, and the icosahedron. Also, three of the five regular polyhedra have vertices where three faces meet — the tetrahedron, the hexahedron (cube), and the dodecahedron. Furthermore, only three different types of polygons comprise the faces of the five regular polyhedra — the triangle, the quadrilateral, and the pentagon.
• There are only three distinct 4×4 panmagic squares.
• Only three tetrahedral numbers are also perfect squares.
• The first number, according to the Pythagoreans, and the first male number.
• The first number, according to Proclus, being the first number such that n² is greater than 2n.
• The trisection of the angle was one of the three famous problems of antiquity.
• Gauss proved that every integer is the sum of at most 3 triangular numbers.
• Gauss proved that for any prime number p (with the sole exception of 3) the product of its primitive roots is ≡ 1 (mod p).
• Any number not in the form of 4ⁿ(8m+7) is the sum of 3 squares.

[edit]In numeral systems

It is frequently noted by historians of numbers that early counting systems often relied on the three-patterned concept of "One- Two- Many" to describe counting limits. In other words, in their own language equivalent way, early peoples had a word to describe the quantities of one and two, but any quantity beyond this point was simply denoted as "Many". As an extension to this insight, it can also be noted that early counting systems appear to have had limits at the numerals 2, 3, and 4. References to counting limits beyond these three indices do not appear to prevail as consistently in the historical record.

[edit]List of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	50	100	1000
	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60	63	66	69	72	75	150	300	3000

Division	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15
	3	1.5	1	0.75	0.6	0.5		0.375		0.3			0.25			0.2
			1			2			3				4			5

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13
	3	9	27	81	243	729	2187	6561	19683	59049		177147	531441	1594323
	1	8	27	64	125	216	343	512	729	1000		1331	1728	2197

[edit]

In science

[edit]Anatomy

• A human ear has three semicircular canals.
• A human middle ear has three ossicles.
• Most elbows consist of three bones, the only joint in the human body where three articulations are surrounded by one capsule.
• Humans perceive white light as the mixture of the three additive primary hues: red, green, and blue.

[edit]Anthropology

According to French historian Georges Duby, the three leaves of the fleur-de-lissymbol represent the three main medieval social classes:
those who prayed,
those who fought and...
those who worked.^[3]

• Georges Dumézil developed the Trifunctional Hypothesis which divides prehistoric Indo-European society into three classes: priests, warriors, and commoners.

[edit]Astronomy

• There are three main galaxy morphological classifications: Ellipticals, Spirals and Lenticulars. These classes are extended for finer distinctions of appearance and to encompass irregular galaxies.
• The Roman numeral III stands for giant star in the Yerkes spectral classification scheme.
• Earth is the third planet in its local Solar System.

[edit]Biology (specific and general)

• Genetic information is encoded in DNA and RNA using a triplet codon system.
• Hemimetabolous insects undergo gradual metamorphosis through three distinct stages: the egg, nymph, and the adult stage, or imago. There is nopupal stage. (Compare to holometabolism which has four stages and is less gradual).
• In paleontology, trilobites are named as such because their bodies are divided in three longitudinal lobes.

[edit]Chemistry

• Three is the atomic number of lithium.
• Atoms consist of three constituents: protons, neutrons, and electrons.

[edit]Physics

• The First Three Minutes: A Modern View of the Origin of the Universe is a book written by Steven Weinberg and published in 1977. It explains the early stages of the Universe.
• The Standard Model of fundamental particles includes three generations of matter (fermions), encompassing the leptons (Generation I—electron; II—muon; III—tau; and their three corresponding neutrinos), and, in pairs of flavors, the quarks (Generation I—up quark & down quark; II—charm quark & strange quark; III—top quark & bottom quark). Thus each of the three generations contains four particles, and these are often shown aligned with four bosons (force-carrying particles) excluding hypothetical bosons such as the gravitonand the Higgs boson.
• A baryon (including protons and neutrons) consists of three quarks.
• We perceive our universe to have three spatial dimensions^{[citation needed]}.
• Three physicists, Albert Einstein, Boris Podolsky and Nathan Rosen (known collectively with the acronym EPR) moved a critique against quantum mechanics publishing the EPR paradox.

[edit]In religion

Many world religions contain triple deities or concepts of trinity, including:

• the Christian Holy Trinity
• the Hindu Trimurti
• the Hindu Tridevi
• the Three Jewels of Buddhism
• the Three Pure Ones of Taoism
• the Triple Goddess of Wicca

[edit]Three major divisions in comparative religion

There are three major divisions in comparative religion:

• Abrahamic religions
• Indian religions (Dharmic) and
• East Asian religions (Taoic).

[edit]Abrahamic religions

The Shield of the Trinity is a diagram of the Christian doctrine of the Trinity

• There are three main Abrahamic religions: Christianity, Islam, and Judaism.

Christianity

• Three people (including Jesus) were crucified at the Crucifixion
• The three Theological virtues referred to 1 Corinthians 13.
• In Roman Catholicism, a group of three martyrs, collectively known as Faith, Hope, and Charity (named after the Theological Virtues).
• Also in Roman Catholic doctrine, there are three realms of the afterlife: Heaven, Hell and Purgatory (Limbo is regarded as hypothetical).
• The three members of the Holy Family: Jesus, Mary, and Joseph.
• The Wise Men who visited Jesus after His birth left Him three gifts.

Islam

• During wudhu, the hands, arms, face and feet are each washed three times.
• According to the prophet Muhammad, there are three holy cities of Islam (to which pilgrimage should be made): Mecca, Medina, andJerusalem.

Judaism

• King Solomon states in Ecclesiastes 4:12: "A three-ply cord is not easily severed." Examples of this concept of three-ness in Judaism are:
  • The three Patriarchs: Abraham, Isaac, and Jacob.
  • The Tanakh has 3 sections: Torah, Nevi'im, and Ketuvim.
  • There are three main divisions of Jews: Kohen, Levi, and Israel (Israelite).
  • Shimon Hatzaddik taught: "On three things the world stands: On Torah, on prayer, and on acts of kindness" (Pirkei Avoth 1:2). Rabban Shimon ben Gamliel taught: "The world continues to exist because of three things: justice, truth, and peace"

[edit]In Buddhism

• The Three Jewels (or Triple Gem) in which Buddhists "take refuge" are the Buddha, the Dharma (the Buddha's teachings), and the Sangha (the community of enlightened beings).
• The Triple Bodhi (ways to understand the end of birth) are Budhu, Pasebudhu, and Mahaarahath.
• The Buddha has three bodies.^{[citation needed]}

[edit]In Hinduism

The "Om" symbol, inDevanagari is also written ओ३म् (ō̄m [õːːm]), where ३ is दीर्घ (dirgha, "three times as long")

• The Trimurti: Brahma the Creator, Vishnu the Preserver, and Shiva the Destroyer.
• The three Gunas underlie action, in the Vedic system of knowledge.

[edit]In Norse mythology

Three is a very significant number in Norse mythology, along with its powers 9 and 27.

• There were three original beings: the primordial cow Audhumla, Ymir the first giant, and Búri the first god and grandfather of Odin.
• Prior to Ragnarök, there will be three hard winters without an intervening summer, the Fimbulwinter.
• Yggdrasil the World Tree has three roots, and three is the square root of the number of worlds (nine) joined by Yggdrasil. Under the three roots are three sacred wells, one for each, including the Well of Urd in Asgard, the Well of Mimir located "among the frost giants", and Hvergelmir in Niflheim.
• Odin endured three hardships upon the World Tree in his quest for the runes: he hanged himself, wounded himself with a spear, and suffered from hunger and thirst.
• During the onset of Ragnarök three cockerels will begin to crow, heralding the final conflict: Gullinkambi for the gods, Fjalar for the giants and an unnamed third for the dead.

[edit]Other religions

• The Wiccan Rule of Three.
• The Triple Goddess: Maiden, Mother, Crone; the three fates.

[edit]In esoteric tradition

• The Theosophical Society has three conditions of membership.
• Gurdjieff's Three Centers and the Law of Three.

[edit]In cartomancy

The three cards spread are used in tarot reading with the first representing the past, the second the present, the third the future.

[edit]As a lucky or unlucky number

This section does not cite any references or sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2009)

Three (三, formal writing: 叁, pinyin san1, Cantonese: saam1) is considered a good number in Chinese culture because it sounds like the word "alive" (生 pinyin sheng1, Cantonese: saang1), compared to four (四, pinyin: si4, Cantonese: sei1), which sounds like the word "death" (死 pinyin si3, Cantonese: sei2).

Counting to three is common in situations where a group of people wish to perform an action in synchrony: Now, on the count of three, everybody pull!  Assuming the counter is proceeding at a uniform rate, the first two counts are necessary to establish the rate, but then everyone can predict when three" will come based on "one" and "two"; this is likely why three is used instead of some other number.

In Vietnam, there is a superstition that considers it bad luck to take a photo with three people in it; it is professed that the person in the middle will die soon.

There is another superstition that it is unlucky to take a third light, that is, to be the third person to light a cigarette from the same match or lighter. This superstition is sometimes asserted to have originated among soldiers in the trenches of the First World War when a sniper might see the first light, take aim on the second and fire on the third.

The phrase "Third time's the charm" refers to the superstition that after two failures in any endeavor, a third attempt is more likely to succeed. This is also sometimes seen in reverse, as in "third man [to do something, presumably forbidden] gets caught".

Luck, especially bad luck, is often said to "come in threes".^[4]

[edit]In philosophy

• The three Doshas (weaknesses) and their antidotes are the basis of Ayurvedic medicine in India.
• Philosophers such as Aquinas, Kant, Hegel, and C. S. Peirce have made threefold divisions, or trichotomies, which have been important in their work.
• Hegel's dialectic of Thesis + Antithesis = Synthesis creates three-ness from two-ness.
• According to Pythagoras and the Pythagorean school, the number 3, which they called triad, is the noblest of all digits, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.^[5]

[edit]In technology

It has been suggested that this article or section be merged into 3 (disambiguation). (Discuss) Proposed since January 2013.

• The resin identification code used in recycling to identify polyvinyl chloride.
• On most telephone keypads, the "3" key is also associated with the letters "D", "E", and "F".